The Department of Chemistry invites you to its upcoming departmental seminar on Monday, January 25, at 4:10 p.m. in Fulmer Hall, room 201.
Abstract: Over the last decade, common, universal properties of complex dynamical systems have been discovered. From protein folding to coupled cell-signaling cascades, many complex systems are characterized by the features of sloppy universality. This universality refers to eigenvalue distributions of the corresponding dynamical matrices that govern complex behavior, which are uniform over the logarithmic scale (exponential spectral decay). For example, in protein dynamics, stiff bond stretch frequencies are overlapping with lower energy frequencies all the way down to ultra-sloppy conformational changes, over 12-15 orders of magnitude.
In modelling complexity of this type, the most important capability is capturing the correct spectral behavior – i.e. the ability to “fit an exponential”. However, fitting an exponential, e.g. with Gaussians or other functions, typically leads to problems that become notoriously ill-conditioned long before the exponential representation can be achieved. In electronic structure, resolving delocalized atomic correlations corresponds to a basis ill-conditioning problem, while modelling delocalized electronic correlations is a gap ill-conditioning problem – these are mathematically equivalent problems by Higham’s identity.
In chemistry and materials science, state of the art algorithms exploit the “near sighted principle” to achieve fast, O(n) methods for large-n systems by truncating interactions that decay as exponentials with interaction distance. Unfortunately, these methods are utterly defeated by the ill-conditioning encountered in the modelling of complex systems, where understanding tail-differences is key.
In this talk, I’ll explain limitations in the state of the art with examples from modelling xylose isomerase, which mediates interconversion between D-glucose and D-fructose, and is interestingly one of the slowest and most economically important enzymes. Then, I’ll show how these ill-conditioned problems can be solved with recently discovered tools that allow to also solve problems in the data sciences, including smooth reconstruction, machine learning and meshfree methods. Finally, I’ll outline ongoing efforts to achieve fast O(n) solvers based on these tools, and to develop opportunities that leverage a common solvers approach to simulation and inference in biochemistry and materials science.
